'\"
'\" Generated from file 'fuzzy\&.man' by tcllib/doctools with format 'nroff'
'\"
.TH "math::fuzzy" n 0\&.2 tcllib "Tcl Math Library"
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.BS
.SH NAME
math::fuzzy \- Fuzzy comparison of floating-point numbers
.SH SYNOPSIS
package require \fBTcl  ?8\&.3?\fR
.sp
package require \fBmath::fuzzy  ?0\&.2?\fR
.sp
\fB::math::fuzzy::teq\fR \fIvalue1\fR \fIvalue2\fR
.sp
\fB::math::fuzzy::tne\fR \fIvalue1\fR \fIvalue2\fR
.sp
\fB::math::fuzzy::tge\fR \fIvalue1\fR \fIvalue2\fR
.sp
\fB::math::fuzzy::tle\fR \fIvalue1\fR \fIvalue2\fR
.sp
\fB::math::fuzzy::tlt\fR \fIvalue1\fR \fIvalue2\fR
.sp
\fB::math::fuzzy::tgt\fR \fIvalue1\fR \fIvalue2\fR
.sp
\fB::math::fuzzy::tfloor\fR \fIvalue\fR
.sp
\fB::math::fuzzy::tceil\fR \fIvalue\fR
.sp
\fB::math::fuzzy::tround\fR \fIvalue\fR
.sp
\fB::math::fuzzy::troundn\fR \fIvalue\fR \fIndigits\fR
.sp
.BE
.SH DESCRIPTION
.PP
The package Fuzzy is meant to solve common problems with floating-point
numbers in a systematic way:
.IP \(bu
Comparing two numbers that are "supposed" to be identical, like
1\&.0 and 2\&.1/(1\&.2+0\&.9) is not guaranteed to give the
intuitive result\&.
.IP \(bu
Rounding a number that is halfway two integer numbers can cause
strange errors, like int(100\&.0*2\&.8) != 28 but 27
.PP
.PP
The Fuzzy package is meant to help sorting out this type of problems
by defining "fuzzy" comparison procedures for floating-point numbers\&.
It does so by allowing for a small margin that is determined
automatically - the margin is three times the "epsilon" value, that is
three times the smallest number \fIeps\fR such that 1\&.0 and 1\&.0+$eps
canbe distinguished\&. In Tcl, which uses double precision floating-point
numbers, this is typically 1\&.1e-16\&.
.SH PROCEDURES
Effectively the package provides the following procedures:
.TP
\fB::math::fuzzy::teq\fR \fIvalue1\fR \fIvalue2\fR
Compares two floating-point numbers and returns 1 if their values
fall within a small range\&. Otherwise it returns 0\&.
.TP
\fB::math::fuzzy::tne\fR \fIvalue1\fR \fIvalue2\fR
Returns the negation, that is, if the difference is larger than
the margin, it returns 1\&.
.TP
\fB::math::fuzzy::tge\fR \fIvalue1\fR \fIvalue2\fR
Compares two floating-point numbers and returns 1 if their values
either fall within a small range or if the first number is larger
than the second\&. Otherwise it returns 0\&.
.TP
\fB::math::fuzzy::tle\fR \fIvalue1\fR \fIvalue2\fR
Returns 1 if the two numbers are equal according to
[teq] or if the first is smaller than the second\&.
.TP
\fB::math::fuzzy::tlt\fR \fIvalue1\fR \fIvalue2\fR
Returns the opposite of [tge]\&.
.TP
\fB::math::fuzzy::tgt\fR \fIvalue1\fR \fIvalue2\fR
Returns the opposite of [tle]\&.
.TP
\fB::math::fuzzy::tfloor\fR \fIvalue\fR
Returns the integer number that is lower or equal
to the given floating-point number, within a well-defined
tolerance\&.
.TP
\fB::math::fuzzy::tceil\fR \fIvalue\fR
Returns the integer number that is greater or equal to the given
floating-point number, within a well-defined tolerance\&.
.TP
\fB::math::fuzzy::tround\fR \fIvalue\fR
Rounds the floating-point number off\&.
.TP
\fB::math::fuzzy::troundn\fR \fIvalue\fR \fIndigits\fR
Rounds the floating-point number off to the
specified number of decimals (Pro memorie)\&.
.PP
Usage:
.CS


if { [teq $x $y] } { puts "x == y" }
if { [tne $x $y] } { puts "x != y" }
if { [tge $x $y] } { puts "x >= y" }
if { [tgt $x $y] } { puts "x > y" }
if { [tlt $x $y] } { puts "x < y" }
if { [tle $x $y] } { puts "x <= y" }

set fx      [tfloor $x]
set fc      [tceil  $x]
set rounded [tround $x]
set roundn  [troundn $x $nodigits]

.CE
.SH "TEST CASES"
The problems that can occur with floating-point numbers are illustrated
by the test cases in the file "fuzzy\&.test":
.IP \(bu
Several test case use the ordinary comparisons, and they
fail invariably to produce understandable results
.IP \(bu
One test case uses [expr] without braces ({ and })\&. It too
fails\&.
.PP
The conclusion from this is that any expression should be surrounded by
braces, because otherwise very awkward things can happen if you need
accuracy\&. Furthermore, accuracy and understandable results are
enhanced by using these "tolerant" or fuzzy comparisons\&.
.PP
Note that besides the Tcl-only package, there is also a C-based version\&.
.SH REFERENCES
Original implementation in Fortran by dr\&. H\&.D\&. Knoble (Penn State
University)\&.
.PP
P\&. E\&. Hagerty, "More on Fuzzy Floor and Ceiling,"
APL QUOTE QUAD 8(4):20-24, June 1978\&. Note that TFLOOR=FL5 took five
years of refereed evolution (publication)\&.
.PP
L\&. M\&. Breed, "Definitions for Fuzzy Floor and Ceiling",
APL QUOTE QUAD 8(3):16-23, March 1978\&.
.PP
D\&. Knuth, Art of Computer Programming,
Vol\&. 1, Problem 1\&.2\&.4-5\&.
.SH "BUGS, IDEAS, FEEDBACK"
This document, and the package it describes, will undoubtedly contain
bugs and other problems\&.
Please report such in the category \fImath :: fuzzy\fR of the
\fITcllib Trackers\fR [http://core\&.tcl\&.tk/tcllib/reportlist]\&.
Please also report any ideas for enhancements you may have for either
package and/or documentation\&.
.PP
When proposing code changes, please provide \fIunified diffs\fR,
i\&.e the output of \fBdiff -u\fR\&.
.PP
Note further that \fIattachments\fR are strongly preferred over
inlined patches\&. Attachments can be made by going to the \fBEdit\fR
form of the ticket immediately after its creation, and then using the
left-most button in the secondary navigation bar\&.
.SH KEYWORDS
floating-point, math, rounding
.SH CATEGORY
Mathematics
